Determine The Equation of a Line
This lesson shows you how to determine the equation of a line by using the given information such as the slope, coordinates of a point, etc.
About This Lesson
In this lesson, we will learn how to determine the equation of a line using the given information.
This lesson will show you two examples on how to do so using the following information:
- Point (2,5) and Slope = 2
- Points (1,4) and (2,1)
You need to have some knowledge on the slope-intercept form of a line. You can learn about it by watching the math video in this lesson.
For the equation of a line that we want to determine, we would usually want that equation to be in the slope-intercept form (see picture).
This way, we just need to use the given information to find the value of the slope (m) and the y-intercept (b).
After doing so, we can easily determine the equation by substituting m and b with their respective value.
Now, watch the following math video to learn more.
Math Video Transcript
Determine the Equation of a Line Transcript
In this lesson, we will learn how to determine the equation of a line, using the available information.
Let's look at the first example. Determine the equation of the line, that passes through the points (2, 5), and with the slope of 2.
To begin, we should know that the equation of a line can be written in the form of y = mx + b, where m is the slope, and b is the y-intercept.
From this, to determine the equation of the line, we just need to find the values of m and b.
Now, we can see that, the slope m, is already given as 2.
Therefore, we can just substitute m with 2, and the equation now becomes y = 2x + b.
Next, we need to find the y-intercept, b.
Since the value of b is not given, we need to find it.
To do so, we know that the line passes through the point 2, 5.
Therefore, we can use this point by substituting x with 2, and substituting y with 5.
With this, notice that we can now solve for b.
To solve for b, multiply 2 with 2. This gives 4.
Next, add negative 4 to both sides of the equation. This gives 5 - 4 = b.
5 minus 4 gives 1. Hence, we found the y-intercept, b as 1.
With this, we can write b as 1.
Finally, since we found both m and b, the equation of the line is y = 2x + 1
Now, next example.
Determine, the equation of the line, that passes through the points (1,4) and (2,1).
Again, we should know that the equation of a line can be written in the form of y = mx + b.
We can see that, the slope and y-intercept are not given. Instead, we only have the coordinates of 2 points.
With some thinking, we can use these 2 points to find the slope 'm' by applying the slope formula, (y2-y1)/(x2-x1).
To use the slope-formula, we can assign this point as point 1, with the x-coordinate as x1, and y-coordinate as y1.
Similarly, we assign the next point as point 2, with x-coordinate as x2, and y-coordinate as y2.
Now, we can find 'm' by just substituting, y2 with 1, y1 with 4, x2 with 2, and x1 with 1.
Alright, we can remove these brackets, as they do nothing.
Let's calculate 'm'. Negative multiply by bracket 4 gives negative 4. negative multiply by bracket 1 gives negative 1.
1 minus by 4 give negative 3. 2 minus by 1 gives positive 1.
Negative 3 divides by positive 1 gives negative 3.
So, we found the slope 'm' as negative 3. Now, we can write m as negative 3.
Next, we need to find the y-intercept, b.
Now, similar to the previous question, we can find b by taking a point on the line, and substitute its x-coordinate and y-coordinate into the equation.
Let's take this point 1,4.
Substituting x with 1 and y with 4.
Now, we can solve for 'b'. Multiplying negative 3 with 1 gives negative 3.
Next, add positive 3 to both sides of the equation. This gives 4 + 3 = b.
4 plus 3 gives 7. Hence, we find the y-intercept, b is 7.
With this, we can now write b as 7.
So finally, with both slope and y-intercept found, we have the equation of the line as, y = negative 3x + 7
That is all for this lesson. Try out the practice question to further your understanding.
Practice Questions & More
Multiple Choice Questions (MCQ)
Now, let's try some MCQ questions to understand this lesson better.
You can start by going through the series of questions on determining an equation of a line parallel to the x-axis or y-axis or pick your choice of question below.
- Question 1 on determining the equation of a line using the coordinates of two points.
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